We call a subset S of a topological vector space V linearly Borel, if for every finite number n, the set of all linear combinations of S of length n is a Borel subset of V . It will be shown that a Hamel base of an infinite dimensional Banach space can never be linearly Borel. This answers a question of Anatolij Plichko. In the sequel, let X be any infinite dimensional Banach space. A subset S ...

A mathematical model is proposed to describe the flow, heat, and mass transfer behaviour of a non-Newtonian (Jeffrey Oldroyd-B) fluid over stretching sheet. Moreover, similarity solution given for steady two-dimensional flow subjected Buongiorno’s theory investigate nature magnetohydrodynamics (MHD) in porous medium, utilizing local thermal non-equilibrium conditions (LTNE). The LTNE based on e...

The motion of microswimmers in complex flows is ruled by the interplay between swimmer propulsion and dynamics induced fluid velocity field. Here we study a chiral microswimmer whose provided spinning helical tail with respect to its body simple shear flow. Thanks an efficient computational strategy that allowed us simulate thousands different trajectories, show shape dramatically affects swimm...

The Folger–Tucker-Equation (FTE) arises from a modification of the Jeffery equation and describes orientation elongated particles in flow by means tensor A. Though FTE represents most widespread commercially used relaxation for A simulations injection molding short-fiber reinforced fluids, analytical solutions formulation applied industry are hardly investigated. Previous work focused on soluti...